8013 PRMIA PRM Exam 1: Finance Foundations Free Practice Exam Questions (2025 Updated)

There was no event such as the CDO squeeze in 2008. (Quite on the contrary, securitized products were selling at distressed prices.).

The silver squeeze of 1979-80 (Hunt brothers), the Chicago fire of 1872 (leading to a short squeeze on wheat), and the wheat squeeze (Hutchingson) of 1866 are real historical events that led to short squeezes in commodity markets. Choice 'b' is therefore the correct answer.

For the PRM exam, you should try to remember the event broadly, and the commodity involved.

The swap can be valued by using the new swap rate of 5%. The investor is paying fixed and receiving LIBOR, and can effectively get out of his position by entering into a swap to receive 5% and pay LIBOR. This will leave him/her with a net cash flow of 1% for two years, ie $1m for 2 years that can be discounted to the present using the rates provided, ie =(1/1.05 + 1/(1.05^2)) = $1,859,410.

Detailed explanation:

An Interest Rate Swap exchanges fixed interest flows for floating rate flows. The floating rate leg is tied to some reference rate, such as LIBOR. The parties exchange net cash flows periodically. Conceptually, an interest rate swap is the combination of a fixed coupon bond and a floating rate note. The party receiving the fixed rate is long the fixed coupon bond and short the FRN, and the party receiving the floating rate is long the FRN and short the fixed coupon bond.

An interest rate swap can be valued as the difference between the two hypothetical bonds. FRNs sell for par at issue time as they pay whatever the current rate is, subject to periodic resets. Therefore immediately after a payment is made on a swap, the value of the FRN component is equal to its par value. The bond can be valued by discounting its cash flows. The difference between the two represents the value of the swap. When the swap is entered into, the fixed rate leg is set in such a way that the value of the hypothetical bond is equal to that of the FRN, and the swap is valued at zero. The rate at which the fixed rate leg is set is called the swap rate. Over its life, market rates change and the value of the fixed coupon bond equivalent in our swap diverges from par (whereas the FRN stays at par - at least right after payments are exchanged and the new floating rate is set for the next period). Thus the swap acquires a non-zero value.

There are two ways to value a swap. If interest rates for the future are known, the bond and the FRN can be valued and their difference will be equal to the value of the swap. Sometimes, the current swap rates are known. In such a case, the swap can be valued by imagining entering into an opposite swap at the new swap rate, which will leave a residual fixed cash flow for the remaining life of the swap. This residual cash flow can be valued and that represents the value of the swap. For example, if a 4 year swap was entered into exchanging an annual fixed 5% payment on a notional of $100m for a floating payment equal to LIBOR, and at the end of year 1 the swap rate is 6%, then the party paying fixed can choose to enter into a new swap to receive 6% and pay LIBOR. All cash flows between the old and the new swap will offset each other except a net receipt of 1% for the next 3 years. This cash flow can be valued using the current yield curve and represents the value of the swap.

Tailing the hedge refers to adjusting the number of futures contracts required to hedge a position given that futures contracts result in daily cash flows from daily P&L. In the case of forward contracts, P&L is not settled daily but at the end of the contract. Because margin payments (ie the daily P&L) for futurescontracts create interest cost or income (depending upon the direction of the flows), the number of contracts required to hedge a given position can fluctuate. This effect is generally small for small positions, or where the time period under consideration is not very long. But it can get large for larger positions that are open for longer time periods, therefore requiring an adjustment to 'tail the hedge'. The adjustment is straightforward - the number of contracts required needs to be divided by (1+r)t, where r is the interest and t the time period (or by ert if continuously compounded rates are being used. Therefore statement I is true and statement II is false.

Statement III is not correct as counterparty risk is certainly an issue for forward contracts, while futures contracts are guaranteed by the exchange, besides having margin requirements and daily P&L movement in place.

Statement IV is not correct as futures come in standardized contracts with standard amounts and a few standard expiry dates to pick, whereas forward contracts are customized and dates, amounts and other details of the contract can be negotiated.

A zero coupon bond has a Macaulay duration equal to its maturity, ie in this case 5 years. We can calculate modified duration from Macaulay duration by using the following relationship:

Modified duration = Macaulay duration/(1 + y) where y is the yield.

Therefore the correct answer is 5 / (1.05) = 4.76.

Or intuitively, all the other answers appear clearly incorrect: 5 and 5.25 are too high, and 4 is too low. Therefore the only reasonable choice is 4.76.

To answer this question, we need to look at the put-call parity, which can be expressed as:

Value of call - Value of put = Spot price - Exercise price discounted to the present

or, Value of call - Value of put = Stock - Bond with a future value equal to exercise price

Therefore, a long call and a short put is equivalent to a long stock position and a short bond.

Choice 'a' is therefore the correct answer. (Alternatively, we could also have constructed a graph of the payoff profiles to arrive at the same answer).

If $x be the spot price of oil, then in order for the forward price to be $75, the following relationship must hold: ($x + $4/(1.06))*(1 + 6%) = $75. Solving, we get x = $66.98

Each of the choices describes various scenarios related to the issue of bonds. A when-issued market is a market in government securities where securities are traded as forward contracts prior to their issue. Choice 'c' is the correct answer.

Choice 'd' refers to a 'bought deal'. Choice 'b' refers to the 'grey market', usually in corporate bonds. Choice 'a' refers to a fixed price re-offer mechanism.

Statement I is true. Consider the Black Scholes PDE 202.23.e1

and substitute delta = 0 (as this is a delta neutral portfolio), and we get the result 202.23.e.

Since r is generally small, and σ and S are positive, theta will be negative when gamma is positive and vice versa.

Statement II is incorrect. The gamma of a call and a put are equal and do not add to 1. The relationship described applies to delta, and not gamma.

Statement III is correct because positive gamma means that the portfolio gains both from an increase and a decrease in the value of the underlying, given delta neutrality. (Generally, a positive gamma is a good thing, but like everything else, it does not come free. A trader can choose to keep their portfolio gamma positive, but in doing so he or she would be giving up premiums from options they would have sold to neutralize the gamma.)

Statement IV is correct because the only way to hedge gamma and vega is through other options positions as only options have gamma and vega. If only one tradeable option is available, it would be possible to hedge either the gamma or the vega, but not both, as achieving neutrality in one will upset the neutrality of the other. The only way to simultaneously hedge the two would be to use two different options on the underlying, and determine the number of options to be traded (using a system of simultaneous equations).

Consider a long vanilla call at a strike of K1, and a short call with a strike price of K2 so that K2>K1. If you construct the payoff diagrams for these option positions, you will see that the combined payoff resembles very closely the payoff of a digital cash-or-nothing option. By bringing K2 and K1 closer together, we can make it very close to a digital cash-or-nothing option. Therefore Choice 'c' is the correct answer.

Statement I correctly describes an IRS.

Statement II is correct - in an IRS the parties do not exchange the principal or the notional amounts as they are in the same currency and can be netted off, but in a currency swap the amounts are in different currencies that cannot be netted (not at least without doing a spot transaction simultaneously), and principals are exchanged.

Statement III is incorrect as the floating rate leg actually is subject to no risk as it resets itself to the current interest rate. The true risk is in the fixed leg which is sensitive to changes in interest rates.

Swaps carry counterparty risks just like any other OTC contract, therefore statement IV is false.

According to the CAPM, the expected return from a risky asset is a function of the contribution of the risky asset to the total risk of the market portfolio. Nothing else matters. All assets are priced according to the risk they bring to the market portfolio, regardless of their individual level of risk. An asset that is very volatile on its own, but has a negative correlation to the market may be priced high, ie have lowexpected return, because of its impact on the risk of the market portfolio. Therefore Choice 'a' is the correct answer, and the other options are incorrect.

Recall that according to the CAPM β = covariancex, y / variancex, where x is the market portfolio and y is the risky asset.

The beta itself is a function of the covariance of the asset's returns with market returns, and therefore only the driver of expected return for an asset is its beta, which is determined by the asset's contribution to portfolio risk. (β = covariance(x, y) / variance(x), where x is the market portfolio and y is the risky asset. )

The put-call parity makes sure that all else remaining equal, an increase in the value of a call option will be accompanies by an increase in the value of the corresponding put option.

Simply stated, the put-call parity can be expressed as:

Value of call - Value of put = Spot price - Exercise price discounted to the present

The two terms on the right hand side of this equation are fixed. Therefore, for the equality to be maintained, any increase in the value of the call option on the left hand side has to be accompanied by the value of the put.

Choice 'c' is therefore the correct answer.

Futures contracts carry no gamma. Only options have gamma. Choice 'a' is the correct answer. Any instrument whose price varies in a linear fashion with respect to the underlying will have gamma equal to zero.

The dates on which the interest rates applicable to the floating rate leg of an IRS are determined are called 'reset dates'. Choice 'c' is the correct answer, the other choices are incorrect. Settlement date is the date a transaction settles, normally a few days after the trade is done depending upon the market. Trade date is the date the terms of the transaction are agreed. (Settlement normally happens on T+n, where T is the trade date, and n the number of days to settlement as decided by agreement or market convention.)

The swap can be valued by valuing the two individual components of the swap.

The fixed rate bond equivalent in the swap is valued at =4/1.05 + 104/(1.06^2) = $96,369,154.

The FRN component will be valued at par as we are at a point where the rate has just been reset, ie $100m.

The investor is paying the fixed rate, and is therefore short the bond. He/she is receiving LIBOR, and is therefore long the FRN. The value of the swap to the investor therefore is +$100,000,000-$96,369,154 = $3,630,846

Detailed explanation:

An Interest Rate Swap exchanges fixed interest flows for floating rate flows. The floating rate leg is tied to some reference rate, such as LIBOR. The parties exchange net cash flows periodically. Conceptually, an interest rate swap is the combination of a fixed coupon bond and a floating rate note. The party receiving the fixed rate is long the fixed coupon bond and short the FRN, and the party receiving the floating rate is long the FRN and short the fixed coupon bond.

An interest rate swap can be valued as the difference between the two hypothetical bonds. FRNs sell for par at issue time as they pay whatever the current rate is, subject to periodic resets. Therefore immediately after a payment is made on a swap, the value of the FRN component is equal to its par value. The bond can be valued by discounting its cash flows. The difference between the two represents the value of the swap. When the swap is entered into, the fixed rate leg is set in such a way that thevalue of the hypothetical bond is equal to that of the FRN, and therefore the swap is valued at zero. The rate at which the fixed rate leg is set is called the swap rate. Over its life, market rates change and the value of the fixed coupon bond equivalent in our swap diverges from par (whereas the FRN stays at par - at least right after payments are exchanged and the new floating rate is set for the next period). Thus the swap acquires a non-zero value.

There are two ways to value a swap. If interest rates for the future are known, the bond and the FRN can be valued and their difference will be equal to the value of the swap. Sometimes, the current swap rates are known. In such a case, the swap can be valued by imagining entering into an opposite swap at the new swap rate, which will leave a residual fixed cash flow for the remaining life of the swap. This residual cash flow can be valued and that represents the value of the swap. For example, if a 4 year swap was entered into exchanging an annual fixed 5% payment on a notional of $100m for a floating payment equal to LIBOR, and at the end of year 1 the swap rate is 6%, then the party paying fixed can choose to enter into a new swap to receive 6% and pay LIBOR. All cash flows between the old and the new swap will offset each other except a net receipt of 1% for the next 3 years. This cash flow can be valued using the current yield curve and represents the value of the swap.

Mortgage backed securities carry prepayment risk as borrowers tend to prepay mortgages when rates fall, and substitute it with newer cheaper mortgages. This creates the issue of 'negative convexity' for mortgages, ie, they lose value when rates rise, but do not gain in value when rates fall.

Prepayment risk can be offset by instruments that also carry negative convexity. A swaption is an option to borrow in the future at an agreed rate, which may be fixed or floating. An option to borrow in the future paying floating and receiving fixed guards against losses when rates fall, as the option can be exercised for a profit when rates are declining and the mortgage portfolio is being prepaid. A callable bond is very similar to an MBS in that the issuer can call it back when rates fall. Thus a long position in an MBS can be offset by a short position in a callable bond. Thus I and III are valid choices.

A cap allows exchanging fixed for floating when interest rates rise above an agreed rate. A long cap position allows borrowing at a fixed rate in exchange for floating, and a short cap implies receiving fixed and paying floating when rates go above the strike rate. Prepayment risk arises from falling interest rates, therefore a short cap will not protect against such a risk as falling interest rates would mean that no payments would be exchanged. Thus II does not help hedge against the risk in question.

A long position in a fixed for floating swap would require paying fixed and receiving floating when rates are falling. This would just make the problem from prepayments worse as the position would pay fixed and receive a falling rate. Thus IV is not an appropriate way to hedge prepayment risk.

This question requires a calculation of the present value of the future cash flows from the bond. The correct answer is $94.92, calculated as =(5/(1 + 5%)) + (5/(1+ 6%)^2) + (105/(1 + 7%)^3).

Backwardation is said to occur when futures prices are lower than the current spot prices. This would happen only when carrying costs are negative. Carrying costs are equal to interest, plus storage costs and less any 'convenience yield'. The existence of large convenience yields may explain backwardation in commodity futures prices. Therefore Choice 'd' is the correct answer.

Contango is the 'normal' market situation where forward prices are higher than spot prices. Storage costs explain contango, not backwardation. Risk free rates, or the cost of funding for the futures position, are always positive and do not explain backwardation.

Investors in CDOs bear credit risk. The SPV is merely a conduit that owns the underlying assets on which the sponsoring institution has bought protection. The investors have sold them this protection, and are on the hook for defaults or other credit events. The reference entity is relevant only to CDSs, not CDOs. Choice 'b' is the correct answer.